Placing spheres in a perfect circle on a ring
Add a single sphere, and a curve to the scene (a Bezier Circle should do). Reduce the size of the sphere down to about 0.1 depending on the scale of the scene you're in.

Next, add an array modifier to the sphere and bump up the counts to about 10 or so you can see something. Finally add a curve modifier to the array of spheres. The spheres should follow the curve and you can now increase the array count depending on the scale of the sphere until both ends meet.

End result:





NB: If after doing this, the spheres don't connect at both ends evenly, just select the sphere in object mode and scale it slightly until they meet. You can also hold Shift while scaling for more precision.

An alternative (but more cumbersome) way is to use dupliframes, see How can I duplicate a mesh along a curve?